Static Rouse modes and related quantities: Corrections to chain ideality in polymer melts

Following the Flory ideality hypothesis intrachain and interchain excluded-volume interactions are supposed to compensate each other in dense polymer systems. Multichain effects should thus be neglected and polymer conformations may be understood from simple phantom chain models. Here we provide evidence against this phantom chain, mean-field picture. We analyze numerically and theoretically the static correlation function of the Rouse modes. Our numerical results are obtained from computer simulations of two coarse-grained polymer models for which the strength of the monomer repulsion can be varied, from full excluded volume ("hard monomers") to no excluded volume ("phantom chains"). For nonvanishing excluded volume we find the simulated correlation function of the Rouse modes to deviate markedly from the predictions of phantom chain models. This demonstrates that there are nonnegligible correlations along the chains in a melt. These correlations can be taken into account by perturbation theory. Our simulation results are in good agreement with these new theoretical predictions.     

Cohesive properties and asymptotics of the dispersion interaction in graphite by the random phase approximation

The structural properties of graphite, such as the interlayer equilibrium distance, the elastic constant, and the net layer binding energy, are obtained using the adiabatic-connection fluctuation-dissipation theorem in the random phase approximation. Excellent agreement is found with the available experimental data; however, our computed binding energy of 48 meV per atom is somewhat smaller than the one obtained by quantum Monte Carlo methods. The asymptotic behavior of the interlayer dispersion interaction, previously derived from analytic approximations, is explicitly demonstrated to follow a d-3 behavior at very large distances.     

Suppression of modes in the random phase approximation

A general but simple method is proposed to eliminate the quantum fluctuations generated by selected one-body operators in the excitation spectrum of a discrete random phase approximation (RPA) Hamiltonian. This method provides an outstanding tool for the removal of the contaminating spurious effects originated from symmetry violations. It can be also applied as a mode filter for analyzing RPA response functions.     

Langevin dynamics of the glass forming polymer melt: Fluctuations around the random phase approximation

In this paper the Martin-Siggia-Rose (MSR) functional integral representation is used for the study of the Langevin dynamics of a polymer melt in terms of collective variables: mass density and response field density. The resulting generating functional (GF) takes into account fluctuations around the random phase approximation (RPA) up to an arbitrary order. The set of equations for the correlation and response functions is derived. It is generally shown that for cases whenever the fluctuation-dissipation theorem (FDT) holds we arrive at equations similar to those derived by Mori-Zwanzig. The case when FDT in the glassy phase is violated is also qualitatively considered and it is shown that this results in a smearing out of the ideal glass transition. The memory kernel is specified for the ideal glass transition as a sum of all “water-melon” diagrams. For the Gaussian chain model the explicit expression for the memory kernel was obtained and discussed in a qualitative link to the mode-coupling equation. Received: 9 January 1998 / Revised: 24 April 1998 / Accepted: 2 July 1998     

Markovian non-Gaussian approximation for light propagation in a random medium

A theory is presented for wave propagation in a random medium that generalizes the Markovian-Gaussian approximation to the case of a non-Gaussian probability distribution of refractivity fluctuations. A Poissonian model of refractivity fluctuations that are statistically independent in non-overlapping intervals in the x-direction is used. This model turns out to be Gaussian under appropriate conditions. General solutions are obtained for the mean field and the mutual coherence function of a plane, partially coherent incident wave. These solutions contain a new functional parameter, a characteristic function of the amplitude of dielectric permittivity fluctuations, that affects the shape of the coherence function as well as its spectrum.     

Extension of the renormalized quasiparticle random phase approximation

The quasiparticle random phase approximation is extended in order to restore of the Pauli principle beyond the renormalized approach by treating the so-called scattering terms in the QRPA phonon operators. It has been shown that this new framework can be described in a case of a single nuclear shell occupied by both protons and neutrons in terms of the QRPA(14,3) algebra. An application of the formalism to the double beta decay of calcium⁴⁸Ca is discussed to some extent. Presented by W.A. Kamiński at the Workshop on calculation of double-beta-decay matrix elements (MEDEX’97), Prague, May 27–31, 1997. This work has been supported in part by the State Committee for Scientific Research (Poland), Contract No. 2 P03B 189 09.     

Numerical solution of the optimized random phase approximation

An accurate, efficient and robust numerical method for the solution of the optimized random phase approximation (ORPA) of classical liquids is presented. The uniqueness of the solution of the ORPA is proved rigorously. The method, hinging on the characterization of the generating functional, improves significantly on previous algorithms. Higher accuracy is obtained by using the values of the unknown functions on the grid points as independent variables instead of the usual coefficients of an expansion in orthogonal polynomials. It is shown that minimizing a suitably modified functional with a conjugate-gradient algorithm results in a very efficient and robust algorithm.     

Nuclear matter properties in the relativistic random phase approximation

Nuclear matter properties at zero temperature are studied in terms of the relativistic σ-ω model, including the random phase approximation (RPA) contribution. At normal density, the medium polarization adds about −35 MeV of binding energy to the mean field result. The scalar and vector effective interaction strengths are fitted to the nuclear matter saturation conditions under various approximations for the energy functional including the RPA term. The effective mass and bulk modulus are calculated with these parameters. The relative importance of different contributions to the binding energy is analyzed.     

Underlying structure of continuum response functions in random phase approximation

It is shown that continuum-RPA results can be understood in terms of energy-dependent, complex RPA states. These states have finite widths which are direct escape widths. Calculations have been performed for a simple model of monopole resonance in ⁴⁰Ca, and the results are compared with those obtained by continuum-RPA and time-dependent Hartree-Fock methods.     

A solvable version of the collisional random phase approximation

We derive the markovian limit of the collisional Random Phase Approximation (CRPA) by resort to the linearization of the Collisional Time-Dependent-Hartree-Fock (CTDHF) equation of motion for the one-body density matrix. The CRPA spectral problem is numerically solved in the frame of a model consisting of a finite fermion system with axial symmetry interacting by means of a separable force. Calculations are performed within a range of interaction strengths, temperature and size parameters and it is shown that both the centroids and the widths of the high energy collective modes exhibit the trend of experimental data.     

Short time corrections to random phase approximation in thermal conduction

Conduction of heat is often described in the random phase approximation (RPA), referring to phonon number but neglecting phases. At is found in several solvable one-dimensional models that there are corrections to RPA at short times t, including a quantum correction which may be irregular as t→0⁺.     

Isovector M6 excitations in the open-shell random phase approximation

OSRPA predictions are made for the excitation energies and transition amplitudes of J^π = 6^?, T = 1 excited states in the even N = Z sd shell nuclei. The results are employed in the calculation of electron scattering form factors. New expressions are given for the double commutators appearing in the OSRPA equations, which greatly facilitate their evaluation.     

Plasma oscillations in fullerene molecules within the random phase approximation

A method is presented for calculating the density of plasma excitation modes in fullerene molecules, which makes it possible to describe more accurately the specific features of the spectra as compared to the models proposed previously. The method is based on the inclusion of the total contribution of π and σ electrons to the spectra of collective oscillations in the molecules. This allows one to consider fullerene molecules with an arbitrary symmetry and arbitrary substituents. A comparative analysis of the experimental curves obtained for resonance electron capture and the results of numerical simulations for C₆₀, C₇₀, and C₇₆ molecules has demonstrated that not only the main maxima but also the ranges of the formation of negative ions coincide.     

水平不变浅海环境随机扰动对声传播的影响

本文主要讨论浅海水平不变波导中的低频声传播问题,为环境适配声纳设计奠定基础。通过仿真分析了海水及海底环境参数对传播损失的影响,根据仿真及实验结果,建立了声速剖面随机扰动及海面、海底起伏条件下的声强分布概率模型,并利用模型中的形状参数α和尺度参数β,提出了局部蒙特卡洛模拟加曲线拟合的声场敏感性分析方法。仿真及实验结果表明声场传播损失服从伽马分布,良好水文条件下10 km距离的声场能量起伏也达到10 d B,随着距离增加,声场敏感性增加。本文所提出方法通过对近场声场的测量和统计实现对远场声场敏感性的预报,与全声场蒙特卡洛模拟相比计算量减小一个数量级。     

Effect of random hydrodynamic inhomogeneities on low frequency sound propagation loss in shallow water

Low frequency (100–500 Hz) sound propagation loss on the US Atlantic continental shelf and in the Barents Sea in the presence of stochastic surface waves, and for the US Atlantic shelf also in the presence of internal waves, is studied for the range of up to 150 km by means of numerical simulations. Qualitative difference between sound propagation loss behavior on the US Atlantic shelf and in the Barents Sea is demonstrated for summertime conditions even without random inhomogeneities. It is shown that whereas internal waves have a weak effect on propagation loss, surface waves result in its considerable increase in both areas under wintertime conditions with a wind speed of more than 9 m/s.     

Energy-weighted sum rule for magnetic excitations in the random phase approximation

The formulas for the energy-weighted sum rule are obtained within the Random Phase Approximation (RPA) in the case of multipole excitations of atomic nuclei induced by the magnetic external field of the general form. The results are compared with the formulas known from the literature and with direct calculations of the moments of the strength function within the RPA.     

Monte carlo studies of phase transitions in polymer blends and block copolymer melts

Summary The unmixing transition of both symmetrical polymer blends AB (i.e. chain lengthsN _A=N _B=N) and asymmetrical ones (N _B/N _A=2,3) is studied by large-scale Monte Carlo simulations of the bond fluctuation model. Combination of semi-grand-canonical simulation techniques, ?histogram reweighting? and finitesize scaling allows an accurate location of the coexistence curve in the critical region. The variation of the critical temperature with chain length (N) is studied and compared to theoretical predictions. For the symmetrical case, use of chain lengths up toN=512 allows a rough estimation of crossover scaling functions for the crossover from Ising to mean-field exponents. The order-disorder transitions in melts of both symmetric (compositionf=N _A/(N _A+N _B)=1/2) and asymmetric (f=3/4) block copolymers is studied for very short chains (16≤N≤60). The interplay between structure and chain configuration is emphasized. Qualitative evidence for ?dumbell formation? of chains and vacancy enrichment in A-B-interfaces and near hard walls is presented. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.